System and method for modulation classification using signal graphs

ABSTRACT

This invention relates system for classifying a modulation format of a communication signal. The system includes a receiving antenna system, to receive the communication signal, a preprocessing module, to evaluate a Fourier transform of a plurality of samples of the received communication signal, normalize each discrete sample of the Fourier transform, quantize each normalized sample based on a number of quantization levels (Q), a graphical analyzer to construct a undirected graph by tracing amplitude of the each quantized sample; and a classification module to extract one or more modulation classification (MC) features from the undirected graph; and to determine the modulation format of the received communication signal based on the extracted MC features.

(1) FIELD OF THE INVENTION

The present invention generally relates to the field of signalprocessing in wireless communications. The present inventionparticularly relates to a method and system for modulationclassification of radio communication signals using signal graphs.

(2) BACKGROUND OF THE INVENTION

Modulation classification (MC) plays an important role in numerousmilitary, civilian and commercial applications such as electronicwarfare, spectrum surveillance, software defined radio (SDR) andcognitive radios. For example, SDRs that can detect, communicate or jama variety of communication standards require automatic recognition ofthe signal modulation employed when no prior knowledge of the incomingsignal is available to perform their function. Generally, MC ischallenging task in a non-cooperative environment, where variousdisturbing factors such as multipath propagation, frequency-selectivityand time-varying nature of the channel exists.

Typically, two classes of MC algorithms exist, likelihood-based (LB) andfeature-based (FB) methods. LB algorithms include a likelihood functionperformed on the received signal, and a decision algorithm performed bycomparing a likelihood ratio against a threshold. Solutions offered byLB algorithms offer a high level of classification performance. However,the solutions suffer from implementational complexity, and sensitivityto model mismatches such as frequency offset, thereby making LBalgorithms unpreferrable in realistic applications. On the other hand,the FB methods are more suitable for practical systems as they aresimpler to implement and more robust to model mismatches. Although theFB methods are not optimal, with appropriate design a near-optimalperformance is achievable.

New generation communication systems are increasingly deployingMultiple-input multiple-output (MIMO) antenna systems due to increaseddata rates and robust communications in multipath fading channels. Whileseveral techniques have been deployed for MC of signals in Single-InputSingle-Output (SISO) systems, only studies have considered MC algorithmsfor MIMO systems in fading channels. For example, the following priorart are provided for their supportive teachings and are all incorporatedby reference. Prior art document, H.-C. Wu, M. Saquib, and Z. Yun,“Novel automatic modulation classification using cumulant features forcommunications via multipath channels,” IEEE Trans. WirelessCommunication., vol. 7, pp. 3098-3105, August 2008(https://ieeexplore.ieee.org/document/4600222/), discloses the use offourth-order cumulant estimators for automatic modulation classification(AMC) of BPSK and QPSK signals over an additive white Gaussian noisechannel. Further, the prior art, includes a nearly minimum-varianceestimator leading to robust AMC features in a wide variety ofsignal-to-noise ratios and without having a priori channel information.However, the disclosed prior art is applicable to SISO systems only andcannot be deployed in communications involving MIMO antenna systems.

Another prior art document, V. D. Orlic and M. L. Dukic, “Automaticmodulation classification algorithm using higher-order cumulants underreal-world channel conditions,” IEEE Commun. Lett, vol. 13, pp. 917-919,December 2009(https://www.researchgate.net/publication/220303345_Automatic_Modulation_Classification_Algorithm_Using_Higher-Order_Cumulants_Under_Real-World_Channel_Conditions),describes use of an AMC algorithm for use in multipath fading channels,based on normalized sixth-order cumulants as MC features. The prior artMC algorithm achieve much better classification accuracy indistinguishing BPSK from complex-valued modulation techniques. However,disclosed prior art cannot be used in MIMO systems.

Another prior art document, M. Marey and O. A. Dobre, “Blind modulationclassification algorithm for single and multiple-antenna systems overfrequency-selective channels,” IEEE Signal Process. Lett., vol. 21, pp.1098-1102, September 2014, describes a blind modulation classification(MC) algorithm applicable to SISO and MIMO systems operating overfrequency-selective channels. A correlation-based approach is proposedin the disclosed prior art, where functions of received signals forcertain modulation formats exhibit peaks at a set of time lags, a resultwhich is exploited as a discriminating feature. However, the disclosedprior art technique suffers from high sensitivity to frequency offsetand requires a long observation interval to achieve desirableperformance.

Another, prior art document U.S. Pat. No. 6,934,342 B1 “AutomaticModulation Type Discrimination Apparatus and Automatic Modulation TypeDiscrimination Method Capable of Discriminating Plural Kinds ofModulation Types”, discloses an AMC technique for detecting themodulation of a received signal. The disclosed technique involves,extraction of a symbol clock and an extension of a signal symbol fromthe received signal for extracting a characteristic of its amplitudedistribution. Based on the extracted characteristic of the amplitudedistribution, it is determined whether the reception signal is a 16 QAMsignal and an M-ary QAM signal of multi-level exceeding 16-levels or anyother signal. Several backtracking and preprocessing of the receivedsignal involved in the disclosed process makes the process timeconsuming and computationally complex.

There is a need for an alternate method and system for detecting MC inmultipath fading channels for both SISO and MIMO systems. Further, thealternate method and system must be computationally less complex andless time consuming. Accordingly, an alternate method and system for MCof signals in communication systems is proposed.

(3) SUMMARY OF THE INVENTION

In view of the foregoing disadvantages inherent in the known methods ofmodulation classification of radio communication signals in multipathfading channels used by SISO and MIMO systems in the prior art, thepresent invention provides an alternate method and system for MC ofsignals based on features extracted over short observation internalsfrom the radio communication signal. As such, the general purpose of thepresent invention, which will be described subsequently in greaterdetail, is to provide a discriminating feature for classification thatis extracted from a graph representation of a Fourier transform of theb_(th) power of samples of the radio communication signal, where b is apositive integer.

An object of the invention is to provide a method for classifying themodulation of a communication signal, received by a receiving antennasystem in a communication network. A Fourier transform of a plurality ofsamples of the received communication signal is evaluated by apreprocessing module. Each discrete sample of the Fourier transform isnormalized and quantized based on several quantization levels(Q).Further, an undirected graph is constructed by a graphical analyzer bytracing the amplitude of each quantized sample. Furthermore, one or moremodulation classification (MC) features is extracted by a classificationmodule from the undirected graph; and the modulation format of thereceived communication signal is determined based on the extracted MCfeatures.

It is another object of the invention to identify a vertex of theundirected graph by an amplitude of a quantized sample and an edge ofthe undirected graph by a transition between amplitudes of a pair ofconsecutive quantized samples.

It is another object of the invention to maintain an edge between a pairof vertices by a probability p>(1−ε)ln(Q)/Q, wherein c is greater thanor equal to a null value.

It is another object of the invention to include several edges of theconstructed undirected graph by a binomial distribution with aprobability distribution function of

It is another object of the invention to construct several undirectedgraphs based on several receiving antennas in the receiving antennasystem.

It is another object of the invention to enable classification of themodulation format of the communication signal in any type of thereceiving antenna system such as a single input single output (SISO)system and a multiple input multiple output (MIMO) system.

It is another object of the invention, to extract by a classificationmodule, one or more modulation classification (MC) features from theundirected graph such as a graph connectivity.

It is another object of the invention, to determine by theclassification module, the modulation format of the receivedcommunication signal by classifying the modulation format into at leastone predefined modulation format based on the extracted graphconnectivity and a formulated binary hypothesis. The predefinedmodulation format may include one of a Binary Phase Shift Keying (BPSK),a Quadrature Phase Shift Keying (QPSK), a Frequency Shift Keying (FSK),and an 8 Phase Shift keying (8PSK).

It is another object of the invention, to select, by the classificationmodule, a hypothesis H0, when the graph connectivity is positive,wherein a positive value of the graph connectivity indicates the graphis connected; and to select a hypothesis H1, when the graph connectivityis negative, wherein a negative value of the graph connectivityindicates the graph is not connected.

In this respect, before explaining at least one embodiment of theinvention in detail, it is to be understood that the invention is notlimited in its application to the details of construction and to thearrangements of the components set forth in the following description orillustrated in the drawings. The invention is capable of otherembodiments and of being practiced and carried out in various ways.Also, it is to be understood that the phraseology and terminologyemployed herein are for the purpose of description and should not beregarded as limiting.

These together with other objects of the invention, along with thevarious features of novelty which characterize the invention, arepointed out with particularity in the disclosure. For a betterunderstanding of the invention, its operating advantages and thespecific objects attained by its uses, reference should be had to theaccompanying drawings and descriptive matter in which there areillustrated preferred embodiments of the invention.

(4) BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood and objects other than those setforth above will become apparent when consideration is given to thefollowing detailed description thereof.

Such description refers to the annexed drawings wherein:

FIG. 1 depicts a block diagram of a system for classifying a modulationformat of a communication signal, according to one of the preferredembodiments of the present invention.

FIGS. 2A to 2D depicts Fourier transform of a first order function of acommunication signal and corresponding undirected graphs, according toone of the preferred embodiments of the present invention.

FIGS. 3A to 3D depicts Fourier transform of a second order function of acommunication signal and corresponding undirected graphs, according toone of the preferred embodiments of the present invention.

FIGS. 4A to 4D depicts Fourier transform of fourth order function of acommunication signal and corresponding undirected graphs, according toone of the preferred embodiments of the present invention.

FIG. 5 depicts a decision tree followed to identifying a modulationformat of a communication signal, according to one of the preferredembodiments of the present invention.

FIG. 6 is a flowchart illustrating a method for classifying a modulationformat of a communication signal, according to one of the preferredembodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description, reference is made to theaccompanying drawings which form a part hereof, and in which is shown byway of illustration specific embodiments in which the invention may bepracticed. These embodiments are described in sufficient detail toenable those skilled in the art to practice the invention, and it is tobe understood that the embodiments may be combined, or that otherembodiments may be utilized, and that structural and logical changes maybe made without departing from the spirit and scope of the presentinvention. The following detailed description is, therefore, not to betaken in a limiting sense, and the scope of the present invention isdefined by the appended claims and their equivalents.

The present invention is described in brief with reference to theaccompanying drawings. Now, refer in more detail to the exemplarydrawings for the purposes of illustrating non-limiting embodiments ofthe present invention.

As used herein, the term “comprising” and its derivatives including“comprises” and “comprise” include each of the stated integers orelements but does not exclude the inclusion of one or more furtherintegers or elements.

As used herein, the singular forms “a”, “an”, and “the” include pluralreferents unless the context clearly dictates otherwise. For example,reference to “a device” encompasses a single device as well as two ormore devices, and the like.

As used herein, the terms “for example”, “like”, “such as”, or“including” are meant to introduce examples that further clarify moregeneral subject matter. Unless otherwise specified, these examples areprovided only as an aid for understanding the applications illustratedin the present disclosure and are not meant to be limiting in anyfashion.

As used herein, the terms “may”, “can”, “could”, or “might” be includedor have a characteristic, that particular component or feature is notrequired to be included or have the characteristic.

Exemplary embodiments will now be described more fully hereinafter withreference to the accompanying drawings, in which exemplary embodimentsare shown. These exemplary embodiments are provided only forillustrative purposes and so that this disclosure will be thorough andcomplete and will fully convey the scope of the invention to those ofordinary skill in the art. The invention disclosed may, however, beembodied in many different forms and should not be construed as limitedto the embodiments set forth herein.

Various modifications will be readily apparent to persons skilled in theart. The general principles defined herein may be applied to otherembodiments and applications without departing from the spirit and scopeof the invention. Moreover, all statements herein reciting embodimentsof the invention, as well as specific examples thereof, are intended toencompass both structural and functional equivalents thereof.Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture (i.e., any elements developed that perform the same function,regardless of structure). Also, the terminology and phraseology used isfor the purpose of describing exemplary embodiments and should not beconsidered limiting. Thus, the present invention is to be accorded thewidest scope encompassing numerous alternatives, modifications andequivalents consistent with the principles and features disclosed. Forpurpose of clarity, details relating to technical material that is knownin the technical fields related to the invention have not been describedin detail so as not to unnecessarily obscure the present invention.

Thus, for example, it will be appreciated by those of ordinary skill inthe art that the diagrams, schematics, illustrations, and the likerepresent conceptual views or processes illustrating systems and methodsembodying this invention. The functions of the various elements shown inthe figures may be provided through the use of dedicated hardware aswell as hardware capable of executing associated software. Similarly,any switches shown in the figures are conceptual only. Their functionmay be carried out through the operation of program logic, throughdedicated logic, through the interaction of program control anddedicated logic, or even manually, the technique being selectable by theentity implementing this invention. Those of ordinary skill in the artfurther understand that the exemplary hardware, software, processes,methods, and/or operating systems described herein are for illustrativepurposes and, thus, are not intended to be limited to any named element.

Each of the appended claims defines a separate invention, which forinfringement purposes is recognized as including equivalents to thevarious elements or limitations specified in the claims. Depending onthe context, all references below to the “invention” may in some casesrefer to certain specific embodiments only. In other cases, it will berecognized that references to the “invention” will refer to subjectmatter recited in one or more, but not necessarily all, of the claims.

All methods described herein can be performed in any suitable orderunless otherwise indicated herein or otherwise clearly contradicted bycontext. The use of all examples, or exemplary language (e.g., “suchas”) provided with respect to certain embodiments herein is intendedmerely to better illuminate the invention and does not pose a limitationon the scope of the invention otherwise claimed. No language in thespecification should be construed as indicating any non-claimed elementessential to the practice of the invention.

Various terms as used herein are shown below. To the extent a term usedin a claim is not defined below, it should be given the broadestdefinition and persons in the pertinent art have given that term asreflected in printed publications and issued patents at the time offiling.

Groupings of alternative elements or embodiments of the inventiondisclosed herein are not to be construed as limitations. Each groupmember can be referred to and claimed individually or in any combinationwith other members of the group or other elements found herein. One ormore members of a group can be included in, or deleted from, a group forreasons of convenience and/or patentability. When any such inclusion ordeletion occurs, the specification is herein deemed to contain the groupas modified thus fulfilling the written description of all groups usedin the appended claims.

The present invention provides a method and a system for modulationclassification (MC) of radio communication signals. A modulation formatof a received signal is determined from MC features that are extractedfrom an undirected graph of a function |Mb(n)|, where |Mb(n)| is aFourier Transform of a bth power of a plurality of samples of thereceived signal. |Mb(n)| is defined as follows:

$\begin{matrix}{{{{M_{b}(n)}} = {{{\mathcal{F}\left\{ {y^{b}(k)} \right\}}} = {{\frac{1}{K}{\sum_{k = 0}^{K - 1}{{y^{b}(k)}e^{{- j}\; 2\pi \; {kn}}}}}}}},} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where y(k) is the kth received sample, k is the number of observedsamples, and F{⋅} represents the discrete Fourier transform of eachsample of the received signal.

Due to independence between transmitted symbols, as K tends to infinity,it is observed that |M_(b)(n)| exhibits peaks at certain values of n,depending on a value of b and a modulation format of the signal. Forexample, |M₂(n)|=|m₂₀Υ| when the modulation format is Binary Phase ShiftKeying (BPSK), where m₂₀ denotes second-order zero-conjugate moment ofthe transmitted modulated symbols and ΥY depends on channelcoefficients. Further, |M₂(n)|=0, when the modulation format isQuadrature Phase Shift Keying (QPSK) and 8 Phase shift keying (8PSK).Hence, |M₂(n)| depends on the modulation format and exhibits peaks atn=0 for certain modulation types based on the value of b.

In order to determine the modulation format of the signal from the MCfeatures that are extracted from an undirected graph, the undirectedgraph needs to be constructed. Typically, the undirected graph isconstructed from the discrete samples |M_(b)(n)|, where n=0, 1 . . .N−1, by executing following three steps:

Step 1: Obtain a normalized sample {tilde over (M)}_(b)(n) for eachdiscrete sample |M_(b)|, where the normalized sample is computed byexecuting equation (2) as shown below:

$\begin{matrix}{{{\overset{\sim}{M}}_{b}(n)} = \frac{{{M_{b}(n)}} - {\min \left\{ {M_{b}} \right\}}}{{\max \left\{ {M_{b}} \right\}} - {\min \left\{ {M_{b}} \right\}}}} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

Step 2: Each normalized sample is quantized with several quantizationlevels (Q).

Step 3: Further, the undirected graph is constructed by tracing anamplitude of the quantized samples. Vertices of the undirected graphrepresent the amplitude of the quantized samples, whereas edges of theundirected graph represent a transition between amplitudes ofconsecutive quantized samples.

Several edges of the undirected graph are used as a measure ofconnectivity of the undirected graph. Based on an Erdos-Reny model ofrandom graphs, in the absence of a significant peak in |Mb(n)|, b=1,2,4,the corresponding constructed graph Gb is connected, and the edgesbetween each pair exists with probability p>(1+ε)ln(Q)/Q, ε≥0. It may benoted that when p=0.5, the connectivity condition is fulfilled for anyvalue of Q. As such, under hypothesis H₀ there are

$N_{Q} = {\begin{pmatrix}Q \\2\end{pmatrix} = {Q{!{{/2}{!{\left( {Q - 2} \right)!}}}}}}$

possible connections (edges) that may occur independently withprobability p>(1+ε)ln(Q)/Q, ε≥0. This implies that the number of edges,E, follows a binomial distribution with the probability density function(pdf)

$\begin{matrix}{{{p_{ɛ}(x)} = {\begin{pmatrix}N_{Q} \\x\end{pmatrix}{p^{x}\left( {1 - p} \right)}^{N_{Q} - x}}},} & {{Equation}\mspace{14mu} (3)}\end{matrix}$

Further, each undirected graph is constructed for each receivingantenna. Hence, in a MIMO system having multiple receiving antennas,multiple undirected graphs can be constructed. Furthermore, hypothesisH₀ is selected if the undirected graph is connected, else hypothesis H₁is selected. Accordingly, a threshold η is set for a certain probabilityof false alarm (Pfa), where P_(fa)=Pr(E^((v))≤η)|H₀), ∀v,0≤v≤N_(r)−1.Typically, P_(fa) is based on a binomial cumulative distributionfunction, as shown in Equation 4, below:

$\begin{matrix}{P_{fa} = {1 - \left( {1 - {\sum\limits_{i = 0}^{\lfloor n\rfloor}{\begin{pmatrix}N_{Q} \\i\end{pmatrix}p^{N_{Q}}}}} \right)^{N_{r}}}} & {{Equation}\mspace{14mu} (4)}\end{matrix}$

where └⋅┘ is the floor function. Even though there is no closed-formexpression for the threshold η, its value can be numerically calculated,e.g., using a bisection method as known in prior art. It may be notedthat the MC feature such as graph connectivity, exists in the presenceof timing and frequency offsets.

FIG. 1 depicts a system 100 deployed in a receiver of a communicationsystem for determining modulation format of a communication signal 110.The system 100 includes a receiving antenna system 102, a preprocessingmodule 104, a graphical analyzer 106, and a classification module 108.The receiving antenna system 102 may be a single input single output(SISO) antenna system or a multiple input multiple output (MIMO) antennasystem. Accordingly, the receiving antenna system 102 may include asingle receiving antenna or multiple receiving antennas. Thecommunication signal 110 may be a radio communication signal receivedover a communication channel when transmitted by a transmit antenna atanother end of a communication network. Alternate forms of communicationsignal 110 can also be envisaged.

The preprocessing module 104 evaluates a Fourier transform of aplurality of samples of the received communication signal 110, andnormalizes each discrete sample of the Fourier transform by executingthe below equation (2)

${{\overset{\sim}{M}}_{b}(n)} = \frac{{{M_{b}(n)}} - {\min \left\{ {M_{b}} \right\}}}{{\max \left\{ {M_{b}} \right\}} - {\min \left\{ {M_{b}} \right\}}}$

Further, the preprocessing module 104 quantizes each normalized samplebased on several quantization levels (Q). The graphical analyzer 106constructs an undirected graph by tracing amplitude of each quantizedsample. Further, the classification module 108 extracts one or moremodulation classification (MC) features from the undirected graph; anddetermines the modulation format of the received communication signal110 based on the extracted MC features. The classification module 108 isfurther configured to extract a graph connectivity as a MC feature fromthe undirected graph. Furthermore, the classification module 108classifies the modulation format into at least one predefined modulationformat based on the extracted graph connectivity and a formulated binaryhypothesis. In an embodiment, the least one predefined modulation formatcomprises a Binary Phase Shift Keying (BPSK), a Quadrature Phase ShiftKeying (QPSK), a Frequency Shift Keying (FSK), and an 8 Phase Shiftkeying (8PSK). In an embodiment, the classification module selects ahypothesis H₀, when the graph connectivity is positive, wherein apositive value of the graph connectivity indicates the graph isconnected. In an embodiment, the classification module selects ahypothesis H₁, when the graph connectivity is negative, wherein anegative value of the graph connectivity indicates the graph is notconnected. The classification of the modulation format can be explainedin reference to an example.

FIG. 2A to 2D, depicts Fourier transform of a communication signal drawnfor |M₁(n)| 201 a for 2-FSK, |M₁(n)| 201 b for BPSK, |M₁(n)| 201 c forQPSK, and |M₁(n)| 201 d for 8-PSK, respectively with single transmitantenna, N_(t)=1, and single receive antenna, N_(r)=1, K=10, 000 signalsamples and 10 dB signal-to-noise ratio (SNR), over the ITU-R pedestrianfading channel. Corresponding undirected graphs G₁ 202 a for 2-FSK, G₁202 b for BPSK, G₁ 202 c for QPSK and G₁ 202 d for 8-PSK are alsodepicted. It can be observed in FIG. 2A, that |M₁(n)| exhibits two peaksonly for 2-FSK, while no peak exists for BPSK, QPSK and 8-PSK as seen inFIGS. 2B-2D respectively. The graphs G₁ 202 b for BPSK, G₁ 202 c forQPSK and G₁ 202 d for 8-PSK are connected with no isolated vertices, dueto absence of a peak in the corresponding |M₁(n)|.

FIG. 3A to 3D illustrates Fourier transform mf a communication signaldrawn for |M₂(n)| 301 a for 2-FSK, |M₂(n)| 301 b for BPSK, |M₂(n)| 301 cfor QPSK, and |M₁(n)| 301 d for 8-PSK, respectively with single transmitantenna, N_(t)=1, and single receive antenna, N_(r)=1, K=10, 000 signalsamples and 10 dB signal-to-noise ratio (SNR), over the ITU-R pedestrianfading channel. Corresponding undirected graphs G₂ 302 a for 2-FSK, G₂302 b for BPSK, G₂ 302 c for QPSK and G₂ 302 d for 8-PSK are alsodepicted. It can be observed in FIG. 3B, that |M₂(n)| exhibits two peaksfor 2-FSK and BPSK, while no peak exists for QPSK and 8-PSK as seen inFIGS. 3C and 3D respectively. The graphs G₂ 302 c for QPSK and G₂ 302 dfor 8-PSK are connected with no isolated vertices, due to absence of apeak in the corresponding |M₂(n)|.

FIG. 4A to 4D illustrates Fourier transform mf a communication signaldrawn for |M₄(n)| 401 a for 2-FSK, |M₄(n)| 401 b for BPSK, |M₄(n)| 401 cfor QPSK, and |M₄(n)| 401 d for 8-PSK, respectively with single transmitantenna, N_(t)=1, and single receive antenna, N_(r)=1, K=10,000 signalsamples and 10 dB signal-to-noise ratio (SNR), over the ITU-R pedestrianfading channel. Corresponding undirected graphs G₄ 402 a for 2-FSK, G₄402 b for BPSK, G₄ 402 c for QPSK and G₄ 402 d for 8-PSK are alsodepicted. It can be observed in FIG. 4C, that |M₄(n)| exhibits a peakfor QPSK, while no peak exists for 8-PSK as seen in FIG. 4D. The graphsG₄ 402 d for 8-PSK is connected with no isolated vertices, due toabsence of a peak in the corresponding |M₄(n)|.

FIG. 5 illustrates decision tree 500 followed for classifying themodulation format of a communication signal. The decision tree 500 canbe designed to classify the modulation format present in discretesamples 502 of a communication signal, into one of the following viz.FSK, BPSK, QPSK and 8-PSK by a formulated binary hypothesis. Forexample, FSK is declared to be present if undirected graph G₁ is notconnected, as illustrated in decision box 504. Further, BPSK is declaredas the modulation format of the communication signal if the graph G₂ isnot connected, as illustrated in decision box 504. Further, QPSK isdeclared to be the modulation format if the graph G₄ is not connected,as illustrated in decision box 504, else 8-PSK is declared to be themodulation format.

FIG. 6 is a flowchart 600 depicting a method for classifying modulationformat of a communication signal, according to an embodiment of thepresent invention.

At 602, a communication signal modulated by a modulation format isreceived by a receiving antenna system. In an embodiment, thecommunication signal may be a radio communication signal and thereceiving antenna system may be a SISO or a MIMO system. In anembodiment, the communication signal may be modulated by one or moreschemes such a Frequency shift keying (FSK), M-ary FSK, Phase ShiftKeying (PSK), Quadrature Phase Shift Keying (QPSK) and 8-PSK, and thelike.

At 604, a Fourier transform of a plurality of samples of the receivedcommunication signal is evaluated by a preprocessing module.

At 606, each discrete sample of the Fourier transform of thecommunication signal, is normalized.

At 608, each normalized sample is quantized based on a number ofquantization levels.

At 610, an undirected graph is constructed by a graphical analyzerpresent in the receiver from the each quantized sample. Each vertex ofthe undirected graph is quantized corresponds to amplitude of aquantized sample. Further, an edge of the graph represents a transitionbetween amplitudes of a pair of quantized samples represented by the twovertices of the edge.

At 612, one or more modulation classification (MC) features can beextracted from the undirected graph. In an embodiment, graphconnectivity is a MC feature that can be extracted.

At 614, a modulation format of the received communication signal isdetermined based on the extracted MC features. For example, if the graphconnectivity is positive, it may indicate that the graph is connected.Further, a hypothesis may be simulated that a connected graph does notrepresent existence of a corresponding modulation format. Accordingly, anegative graph connectivity indicates that the graph is not connected,thereby indicating existence of peaks in the corresponding discreterepresentation of the signal. Existence of peaks indicate existence of acorresponding modulation format. Examples of modulation formats isexplained in reference to FIGS. 2A-4D.

It is to be understood that the above description is intended to beillustrative, and not restrictive. For example, the above-discussedembodiments may be used in combination with each other. Many otherembodiments will be apparent to those of skill in the art upon reviewingthe above description.

The benefits and advantages which may be provided by the presentinvention have been described above with regard to specific embodiments.These benefits and advantages, and any elements or limitations that maycause them to occur or to become more pronounced are not to be construedas critical, required, or essential features of any or all of theembodiments.

While the present invention has been described with reference toparticular embodiments, it should be understood that the embodiments areillustrative and that the scope of the invention is not limited to theseembodiments. Many variations, modifications, additions and improvementsto the embodiments described above are possible. It is contemplated thatthese variations, modifications, additions and improvements fall withinthe scope of the invention.

1. A method comprising: receiving, by a receiving antenna system, acommunication signal modulated by a modulation format; evaluating, by apreprocessing module, a Fourier transform of the bth power of aplurality of samples of the received communication signal, where b is apositive integer; normalizing, by the preprocessing module, eachdiscrete sample of the Fourier transform; quantizing, by thepreprocessing module, each normalized sample based on a number ofquantization levels (Q); constructing, by a graphical analyzer, anundirected graph by tracing amplitude of the each quantized sample;extracting, by a classification module, one or more modulationclassification (MC) features from the undirected graph; and determining,by the classification module, the modulation format of the receivedcommunication signal based on the extracted MC features; whereinextracting, by a classification module, one or more modulationclassification (MC) features from the undirected graph, furthercomprises extracting a graph connectivity as a MC feature from thegraph.
 2. The method of claim 1, wherein a vertex of the undirectedgraph represents an amplitude of a quantized sample.
 3. The method ofclaim 2, wherein an edge of the undirected graph represents a transitionbetween amplitudes of a pair of consecutive quantized samples.
 4. Themethod of claim 3, wherein an edge between a pair of vertices existswith a probability p>(1−ε)ln(Q)/Q, wherein ε is greater than or equal toa null value.
 5. (canceled)
 6. The method of claim 1, wherein a numberof constructed graphs is based on a number of receiving antennas in thereceiving antenna system.
 7. The method of claim 1, wherein thereceiving antenna system is one of a single input single output (SISO)system and a multiple input multiple output (MIMO) system.
 8. (canceled)9. The method of claim 1, wherein determining, by the classificationmodule, the modulation format of the received communication signal,further comprises: classifying the modulation format into at least onepredefined modulation format based on the extracted graph connectivityand a formulated binary hypothesis.
 10. The method of claim 9, whereinthe at least one predefined modulation format comprises a Binary PhaseShift Keying (BPSK), a Quadrature Phase Shift Keying (QPSK), a FrequencyShift Keying (FSK), and an 8 Phase Shift keying (8PSK).
 11. The methodof claim 9, further comprising: selecting, by the classification module,a hypothesis H₀, when the graph connectivity is positive, wherein apositive value of the graph connectivity indicates the graph isconnected; and selecting, by the classification module, a hypothesis H₁,when the graph connectivity is negative, wherein a negative value of thegraph connectivity indicates the graph is not connected.
 12. A systemcomprising: a receiving antenna system configured to receive acommunication signal modulated by a modulation format; a preprocessingmodule configured to: evaluate a Fourier transform of the bth power of aplurality of samples of the received communication signal, where b is apositive integer; normalize each discrete sample of the Fouriertransform; quantize each normalized sample based on a number ofquantization levels (Q); a graphical analyzer configured to: constructan undirected graph by tracing amplitude of the each quantized sample;and a classification module configured to: extract one or moremodulation classification (MC) features from the undirected graph andextracting a graph connectivity as a MC feature from the graph; anddetermine the modulation format of the received communication signalbased on the extracted MC features.
 13. The system of claim 12, whereina vertex of the undirected graph represents an amplitude of a quantizedsample.
 14. The system of claim 13, wherein an edge of the undirectedgraph represents a transition between amplitudes of a pair ofconsecutive quantized samples.
 15. The method of claim 3, wherein anedge between a pair of vertices exists with a probabilityp>(1−ε)ln(Q)/Q, wherein ε is greater than or equal to a null value. 16.(canceled)
 17. The system of claim 12, wherein a number of constructedgraphs is based on a number of receiving antennas in the receivingantenna system.
 18. The system of claim 12, wherein the receivingantenna system is one of a single input single output (SISO) system anda multiple input multiple output (MIMO) system.
 19. (canceled)
 20. Thesystem of claim 19, wherein the classification module, is furtherconfigured to: classify the modulation format into at least onepredefined modulation format based on the extracted graph connectivityand a formulated binary hypothesis.
 21. The system of claim 20, whereinthe at least one predefined modulation format comprises a Binary PhaseShift Keying (BPSK), a Quadrature Phase Shift Keying (QPSK), a FrequencyShift Keying (FSK), and an 8 Phase Shift keying (8PSK).
 22. The systemof claim 20, further comprising: selecting, by the classificationmodule, a hypothesis H₀, when the graph connectivity is positive,wherein a positive value of the graph connectivity indicates the graphis connected; and selecting, by the classification module, a hypothesisH₁, when the graph connectivity is negative, wherein a negative value ofthe graph connectivity indicates the graph is not connected.